Curiosity could be simply stated as the "urge to find-out". It is the basic instinct of every animals to find out about that thing, which in some way attracts/fascinate them. it is the curiosity that increases the intelligence and knowledge of an individual. Curiosity is also the root cause for discoveries.

It could be constructive and destructive depending on the situation. Curiosity when becomes obsession or nosey is bad. Hyper-curiosity creates feeling of irritation in other people. Reckless curiosity can put one in dangerous surroundings or cause accidental hazards. in this way curiosity could be destructive.

Curiosity is very essential in learning. One may be able to memorize certain amount of information, but to "learn", curiosity is needed. Things learned of curiosity are better and easily understood and kept in memory for longer. Curiosity increases the knowledge and intellect in both qualitative and quantitative scales.

I like your answer. ( I have not been back to this website for a while. )

How is curiosity generated?

By asking questions.

But asking questions is not encouraged by teachers.

What if teachers had to assess their students by the questions they asked rather than by their answers?

This is my favorite topic! It is innate, yet dies. It is constructive but can be very destructive (smoking, method, etc.) And yes, it is squashed by much of education, replaces instead by achievement and extrinsic rewards like stars, gift bags, and pizza parties.

If curiosity entails the tendecy to explore, the reason why so many creatures have evolved/developed it should be connected to the survival of the particular species. Exploration can lead you to find food or a safe place to dwell. On the other hand, it can help you discover what's behind your back and might hurt you in the future.

Eleanna, I like your idea of linking curiosity with a core survival strategy. I have just read Restless Creatures by Matt Wilkinson which you might enjoy too. A story of evolution told through a very readable history of how and why creatures move the way they do.Then I was recalling how when I worked on a farm, I noticed that every few years or so there would be a calf or lamb or chicken that stood out from the rest, that showed more curiosity than their herd. Looked up this proverb and learned something new! 

"Curiosity killed the cat" is a proverb used to warn of the dangers of unnecessary investigation or experimentation. A less frequently-seen rejoinder to "curiosity killed the cat" is "but satisfaction brought it back".

The original form of the proverb, now little used, was "Care killed the cat". In this instance, "care" was defined as "worry" or "sorrow." (Wikipedia)

This book certainly looks very interesting.

The history of the proverb can be quite telling. Worry can be connected to curiosity as a need to investigate a potential danger (the 'what's behind your back' part, hence the connection of worry with fear). Could explain why some intensely curious people are also worrywarts, while a lot of 'laid back' people more easily intellectually satisfied.

Was not expecting an answer, thank you for getting back.